The Physics of Solid Density Plasmas Created by Intense X-Ray Free Electron Lasers

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The Physics of Solid Density Plasmas Created by Intense X-Ray Free Electron Lasers

Justin Wark

Department of Physics Clarendon Laboratory

&

Trinity College University of Oxford, UK justin.wark@physics.ox.ac.uk

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Outline

‣ Motivation: creating ‘warm dense matter’.

‣ The choice of aluminium.

‣ First Experiments on FLASH at 92 eV.

‣ Making transparent aluminium (saturable absorption in the XUV).

‣ The electronic structure of warm dense matter.

‣ The energy budget.

‣ Experiments on LCLS at 1400 - 1800 eV.

‣ Measuring Ionisation Potential Depression (Al, Mg, Si)

‣ DFT Theory of IPD

‣ Saturable absorption at > 1500 eV.

‣ First measurements of collisional ionisation rates at solid densities.

‣ Creation of uniform, optically-thin solid-density plasmas ~120 atoms across.

‣ Historical context: re-climbing Moseley’s ladder.

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Outline

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High energy-density systems: Warm and Hot Dense Matter

Hydrogen Phase Diagram Aluminium Phase Diagram

= V _Coulomb

E _Kinetic ⇡ 1

classical plasma

dense plasma

high density matter Γ = 1

Γ = 10

Γ = 100

Density ( g/cm3)

103 104

101 102

102 104 10010-4 10-2 1

WDM

T e m p e ra tu re ( e V )

Temperatur e (eV) Temperatur e (eV)

Density (g/cm

³

) Density (g/cm

³

)

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Outline

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K-edge L-edge

ω_p

σ_ff

(µm-1)

E_phot

1s² 3s² 3p¹

2p⁶

2s² 2p⁶

K: 1s² L: 2s² 2p⁶

Neutral Al

Electronic structure of Aluminium (Z=13)

Aluminium has a relatively simple Neon-like core, but already displays ‘plasma’ conducting behaviour as a trivalent prototypical metal. The atomic physics is simple enough to be tractable, yet complex enough to be interesting.

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Outline

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Irradiating thin (50-nm) Al with intense (> 10

¹⁶

Wcm

^-2

) XUV (92eV) light

Focusing optic:

multilayer coated off-‐

axis parabola

FLASH

Position of a ToF

Focused on Targets:

PMMA, Ce:YAG, Al, SiN,

CHAMBER ATTACHED TO FEL

OAP

GM

Diode Al sample

λ=13.5nm 5

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K-edge L-edge

ω_p

σ_ff

(µm-1)

E_phot

1s² 3s² 3p¹

2p⁶

2s² 2p⁶

FLASH

K: 1s² L: 2s² 2p⁶

Photo-ionization

Neutral Al

Electronic structure of Aluminium

L=shell lifetime ~40 fs

92eV photon

73eV

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Ejection of the L shell electron shifts the L-edge

K: 1s² L: 2s² 2p⁶

Photo-ionization ^73eV

92eV photon

K: 1s² L: 2s² 2p⁶

Photo-ionization ^93eV

92eV photon

The reduced shielding shifts the L-edge, and photons can no longer be absorbed until the electron recombines with a lifetime of 40-fs, but this is

longer than the 15-fs pulse length.

Meanwhile, the electron starts to

thermalise with the Fermi sea, heating it up.

X

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Saturation of L-shell holes, and homogeneous isochoric heating

The plot shows the percentage of atoms with an L-shell hole at the end of the 15-fsec pulse.

Note 100% is reached at fairly low fluences - but the transmission is still not very high at such a fluence, because we are plotting the

transmission integrated in time, and there is always relatively high absorption

at the start of the pulse.

The saturable absorption leads to much more uniform energy deposition within the fold

10

0 2 4 6 8

Time (fs)

Sample Depth(nm)

0 50

0 5 10 15

25

0 5 10 15

Te (eV)

Nature Physics 5, 693 (2009)

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Outline

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Probing the electronic structure of a solid density plasma

Al 4+

Al 3+

Al 3+ Al 3+

Al 3+

Al 3+ Al 3+

Al 3+

Al 4+

Al 4+ Al 4+

Al 4+

Al 4+ Al 4+

Al 3+

K: 1s² L: 2s² 2p⁶

Recombination

Low Intensity XUV Laser

High Intensity XUV Laser

The environment surrounding the recombining ion changes with

increasing saturation, and the average free electron density changes from 3+ to 4+. This will alter the electronic structure (the density of states) and therefore the observed XUV emission spectrum, where we see fluorescence as electrons recombine from the continuum.

Density of States

DOS ~√E

Recombination observed in fluoresence

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Probing the electronic structure of a solid density plasma

The emission spectra show the shape of the density of states of the ionised plasma. The inferred temperatures will be below those predicted to exist at the end of the pulse, as the continuum electrons are heated by the Auger eﬀect as recombination occurs.

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Outline

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Energy Budget: Highest Intensities

1s² 2s²2p⁶

Solid Al n(E)

E Free electrons

E_F=11eV

+ 92eV =

1s² 2s²2p⁶ n(E)

E

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Energy Budget: Highest Intensities

1s² 2s²2p⁶ n(E)

E

2s²2p⁶

1s² n(E)

E Auger decay +

collisions 20eV

1s² 2s²2p⁶ n(E)

E fsec collisions

7eV

Solid Density

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Energy Budget: Highest Intensities

2s²2p⁶

1s² n(E)

E 20eV

2s²2p⁶

1s² n=3 n=4 3 e in continuum

Atomic, Al IV , about 6eV

Electron-ion coupling Expansion on psec timescales

Observe bound- bound transitions

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Energy Budget: Highest Intensities

•

After several picoseconds we expect the target to disassemble, and see atomic spectra. We only see Al IV lines, consistent with assumed final temperatures of order 6-eV. Little evidence of Al V.

Al IV, 2s²2p⁶ - 2s²2p⁵3s

Al IV, 2s²2p⁶ - 2s²2p⁵3d

FEL Beam

Phys. Rev. Lett, 106, 164801 (2011)

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Outline

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The experiment at the Linac Coherent Light Source X-ray Free-Electron Laser

X-ray spectrometer: K-alpha emission Al around 1500 eV LCLS pulse

Photon energy: 1460–1830 eV Pulse length < 60 fs

Pulse Energy ~1.5 mJ Bandwidth ~ 0.4%

Diode Bragg

crystal

1 micron thick Al sample

Vinko et al., Nature 482, 59 (2012) Ciricosta et al., PRL 109, 065002 (2012)

CCD

Peak Intensity ~10¹⁷W cm^-2

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K-edge L-edge

ω_p

σ_ff

(µm-1)

E_phot

1s² 3s² 3p¹

2p⁶

2s² 2p⁶

LCLS

K: 1s² L: 2s² 2p⁶

Photo-ionization

Neutral Al

Electronic structure of Aluminium

Core-hole lifetime ~1fs

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K-edge L-edge

ω_p

σ_ff

(µm-1)

E_phot

1s² 3s² 3p¹

2p⁶

2s² 2p⁶

LCLS

Neutral Al

K: 1s¹ L: 2s² 2p⁶

K-alpha emission

Electronic structure of Aluminium

Core-hole lifetime ~1fs

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Electronic structure of Aluminium

Ionized Al: e.g. 6+

Neutral Al:

K: 1s² L: 2s² 2p³

K: 1s¹ L: 2s² 2p⁶

Note that both the K-edge energy, and the K-α energy increase with increasing charge state.

K-edge

K-α

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The FEL creates core holes, and the dominant heating is Auger

Ionized Al: e.g. 6+

K: 1s² L: 2s² 2p³

Energies not to scale!

K: 1s² L: 2s² 2p³

Important to note: the heated continuum - many tens of eV, can further collisionally ionise the system.

No K-α will be seen if the K-edge energy of an ion exceeds the photon energy of the X-Ray Laser.

Temperature of plasma insuﬃcient to excite n=2. We only see the K-shell emission while th x-ray laser is on.

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If the FEL photon energy is too low, no K-a generated Ionized Al: e.g. 6+

K: 1s² L: 2s² 2p³

Tuned FEL photon energy

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K-shell spectroscopy of Hot Dense Aluminium

IV V VI VII VIII IX X XI V VI VII VIII IX X

Emitted photon energy (eV)

Energy of x−ray FEL excitation (eV)

1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1475

1500 1525 1550 1575 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825

Resonant transitions

Cold K-edge

Single K-shell hole Double K-shell hole

Nature 482, 59 (2012)

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K-shell spectroscopy of Hot Dense Aluminium

IV V VI VII VIII IX X XI V VI VII VIII IX X

1475 1500 1525 1550 1575 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825

Cold K-edge

Single K-shell hole Double K-shell hole

K-edge energies

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Isochoric heating: plasma evolution

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Charge state 0.00

0.05 0.10 0.15 0.20 0.25 0.30 0.35

Fractional yield integrated over pulse

1580 eV 1630 eV 1680 eV 1730 eV 1780 eV 1830 eV

0 20 40 60 80 100 120 140 160

Time (fs) 1^x10²³

2^x10²³ 3^x10²³ 4^x10²³ 5^x10²³ 6^x10²³

Density (electrons cm-3 )

0 20 40 60 80 100 120 140 160

Time (fs) 0

50 100 150 200

Temperature (eV)

The FEL reveals charge states when its energy exceeds the K-edge - the charge state distribution itself does not vary that greatly with photon energy.

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K-shell spectroscopy of Hot Dense Aluminium

VII

1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1475

1500 1525 1550 1575 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825

IV

1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680

1475 1500 1525 1550 1575 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825

K shell L shell

Continuum

L shell

K shell

FEL photon energy

0

Continuum

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Continuum lowering in dense plasmas

Figure taken from

Umstadter, Physics 5, 88 (2012)

Isolated atom

In dense systems at some radius outer orbitals may overlap – these can no longer be considered bound to a specific ion = ionised.

This means the energy required to ionise a bound state is reduced as the density increases:

Ionization Potential Depression (IPD)

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‣ Analytical models used when fast calculations required (atomic kinetics, hydrodynamic codes, etc.):

‣ Ion-sphere (compute total energy of free electron in Wiegner-Seitz ion sphere, originates from condensed matter theory):

‣ Debye Hückel (calculate electrostatic energy of electron/ion + Debye cloud, works in weak- coupling):

‣ Stewart & Pyatt model, 1996, used in almost all atomic kinetics models (bridges between the two above):

‣ Ecker & Kröll model, 1963, (diﬀerent Z scaling, matches LCLS data)

Some simple Ionization Potential Depression models

I

_IS

= 3 2

ze

²

4⇡✏

₀

r

_SP

I = C ze

²

I

_SP

= k

_B

T

2(z

^⇤

+ 1)

(✓ 3(z

^⇤

+ 1)ze

²

4⇡✏

_{0 D}

k

_B

T + 1

◆

2/3

1 ) I

_DH

= ze

²

4⇡✏

_{0 D}

4⇡

3 r³_SP = n_i ¹

4⇡r³ = 1

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‣ Analytical models used when fast calculations required (atomic kinetics, hydrodynamic codes, etc.):

‣ Ion-sphere (compute total energy of free electron in Wiegner-Seitz ion sphere, originates from condensed matter theory):

‣ Debye Hückel (calculate electrostatic energy of electron/ion + Debye cloud, works in weak- coupling):

‣ Stewart & Pyatt model (bridges between the two above):

‣ Ecker & Kröll model (diﬀerent Z scaling, matches LCLS data)

Some simple Ionization Potential Depression models

I

_IS

= 3 2

ze

²

4⇡✏

₀

r

_SP

I

_EK

= C ze

²

4⇡✏

₀

r

_EK

I

_SP

= k

_B

T

2(z

^⇤

+ 1)

(✓ 3(z

^⇤

+ 1)ze

²

4⇡✏

_{0 D}

k

_B

T + 1

◆

2/3

1 ) I

_DH

= ze

²

4⇡✏

_{0 D}

4⇡

3 r³_SP = n_i ¹

4⇡

3 r_EK³ = 1 n_e + n_i

Preston et al., HEDP 9, 258 (2013)

Based on Debye screening: at solid density there is

less than 1 electron per Debye sphere!

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1500 1550 1600 1650 1700 1750 1800 Photon energy (eV)

1x10⁴ 1^x10⁵ 1x10⁶ 1^x10⁷

Emission (phot/eV/sterad)

IV VVI VII

Resonant emission peaks Ionization thresholds

If we can identify these thresholds with K-edges, then:

Experimental IPD = Atomic edge - Measured edge

Experimental measurement of IPD on LCLS

1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1475

1500 1525 1550 1575 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825

IV V VI VI VI IX X XI V VI VI VI IX X

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justin.wark@physics.ox.ac.uk

Experimental measurement of IPD on LCLS

L shell into the vacant K-shell state. That is to say that we are not reliant on observing emission from states very close to the continuum, that are subject to significant line broad- ening, in order to determine whether or not ionization has occurred.

We model our experimental results with atomic kinetics simulations using the collisional-radiative superconfigura- tion code SCFLY [20]. The code is specifically tailored to x-ray laser related problems, and has previously been tested in the noncollisional regime [21]. It uses a rate equation formalism to calculate the time evolution of the atomic populations, taking into account the effects of the IPD for the different ionization stages, and provides as an output the time resolved temperature, density, CSD, opacity and emission spectra. We have incorporated the SP (the full analytical model as in Ref. [2]) and EK models of IPD within the code. The spatial variation in intensity across the approximately 9:1 ! 0:8 !m² area of the LCLS focal spot was taken into account, by appropriately summing and weighting simulations at different intensities, with the spatial profile of the focal spot determined by laser im- prints in PbWO₄ taken during the experiment [22].

A comparison between the experimental and simulated spectra is shown in Fig. 1. It can be observed that the SP calculations do not correctly reproduce the dependence of the K-" spectra on the LCLS photon energy, while the EK model provides excellent agreement in reproducing the appearance, intensity, and positions of the various K-"

peaks. For example, the SP model cannot predict the appearance of the V K-" line at an LCLS photon energy of 1580 eV, the VI line (at 1630 eV), or the lines X and XI (at 1830 eV). In contrast the EK model provides a striking agreement with the experimental K-" spectra.

In Fig.2 we plot the experimentally detected and calculated K edges, and the corresponding IPD values, for the first five charge states. The experimental K edges are determined by the appearance of the peaks in the spectra as a function of the LCLS photon energy, while the calculated ones are given by simulations performed at photon energies given by the experimental edges, taking the edge value at the time where the corresponding line emission is maximum. The last three charge states are not shown because determining the K-edge position for these lines is complicated by the presence of the overlapping K-#

series. The calculated energies of the shells of the free ions are also shown, demonstrating that only the K and L shell states are bound at these densities within the EK model.

The experimental IPD values shown on the right part of the figure are determined by the difference between the atomic and detected edge values, while the solid colored parts of the histograms’ bars for the simulated values illustrate the variation of the IPD as the electron density increases during the evolution of the system. The success of the EK calculations compared with those employing the SP model is clear.

The IPD has an influence not only on the number of K-"

peaks observed, but also on the energy at which they are emitted. For highly charged Al ions, as can be seen in Fig.2 for the charge states VII and VIII, the SP model predicts a far smaller IPD, so that the lowest energy of the continuum is such that the M shell rebinds, resulting in greater screening of the L-shell electrons, and a shift in the K-" energy [23]. In contrast, the larger IPD predicted by EK means that the M shell is pressure ionized for all the ions (as in the cold solid). The effect of this difference can be seen again in Fig. 1, where the arrows under the spectrum corresponding to 1830 eV pumping show that the simulations using the SP model predict the wrong position for the VII–XI K-" lines, while the EK model agrees with experiment; i.e., the data demonstrate that the M shell is indeed pressure ionized.

This effect explains the discrepancies in the energies of the K-" lines in the simulations presented in [19], which used a modified version of the SP model.

As additional evidence, in Fig. 3 we plot the spectra showing the secondary K-" series, corresponding to the emission from atoms with a doubly ionized K shell [24].

Since the energy threshold values for ionizing a second electron from the K shell are higher than the K edges for the main satellite series, the progressive appearance of these lines occurs at higher pump photon energies. The four lines shown are emitted from the same ion stages responsible for the emission of the lines V–VIII in the main series, so the

1450 1500 1550 1600 1650 1700 1750 1800 Energy from K-shell (eV)

IV V VI VII

VIII L M

50 100 150 IPD (eV)

EK SP exp

continuum atomic edge SP edge EK edge range of

experimental edge

FIG. 2 (color online). Left—The grey region shows the continuum for different charge states, as determined from the experimental spectra in Fig. 1, with the dark grey region corresponding to the observed range of the K edge. The values given by the SP and EK calculations correspond to the edges calculated at the time of maximum emission for each associated K-" line.

The calculated energy to pump a K-L and K-M transition (for the same number of L shell electrons in the final state) is also indicated. Right—IPD values; the darker colored zones of the histogram correspond to the IPD variation detected, for the experimental bars, and to the total IPD variation during the system evolution, for the simulated ones.

PRL 109, 065002 (2012) P H Y S I C A L R E V I E W L E T T E R S week ending 10 AUGUST 2012

Single core holes Double core holes

Note: M-shell always in continuum according to EK model.

Note: we do NOT claim EK model is ‘correct’, only that it fits this case. It is also a crude semi-classical model.

~50 eV!

35

Phys. Rev. Lett, 109, 065002 (2012)

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Modelling the date via collisional-radiative super-configuration code SCFLY

‣ Proven to work in modelling intense X-ray interaction with atoms in the collision-less regime

‣ All super-configurations up to n=3 included with appropriate degeneracy

‣ Self-consistent temperature calculated via X-ray deposition within duration of pulse

‣ Spectral synthesis via a super-configuration transition array model

‣ Included opacity via escape factor formalism, IPD via IS, SP and EK models

‣ We perform simulations at 24 intensities, and weight them according to experimentally measured profiles of the x-ray focal spot.

‣ There is no fit to the data - we simply run the code for the experimental photon energy and intensities, and simulate the spectrum.

‣ The only adjustable part is the model for ionisation potential depression

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Ciricosta et al., PRL 109, 065002 (2012)

1580 eV 1600 eV 1630 eV 1650 eV 1720 eV 1830 eV

LCLS pump energy:

Continuum lowering results on LCLS

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Outline

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Continuum lowering via Density Functional Theory

‣ There is a fundamental problem with the way we think of continuum lowering

‣ cannot explain the experimental observations: EK works only in some cases, SP only in others

‣ we seem to be missing some physics

‣ Treatment of shells near continuum (M-shell) in analytical models is very poor

‣ models need a sharp cutoﬀ to what is physically a continuous process

‣ states within a shell not always treated individually

‣ we should not need to artificially separate states into ‘bound’ and ‘free’

‣ Lets try a diﬀerent approach that we know works for ground-state metals:

‣ Calculate IPD independent of a specific analytical model

‣ Want the results to be consistent with relevant atomic physics and thermodynamics

‣ Applicable to the plasma conditions reached on LCLS

‣ Extend beyond the average atom picture, and we do NOT assume spherical symmetry.

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Continuum lowering via DFT - simulation box

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7

⁺

7

⁺

Continuum lowering via DFT - add the ions

6

⁺

6

⁺

6

⁺

4

⁺

5

⁺

PAW Potentials to simulate ion core + inner shell bound electron states

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7

⁺

7

⁺

Continuum lowering via DFT - add electrons

6

⁺

6

⁺

6

⁺

4

⁺

5

⁺

Box should be charge neutral (here we need 41 electrons)

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Excited state PAW potentials

‣ Core-excited (rather than ionised) = global charge neutrality of the system

‣ PAW (projector augmented wave) formalism is key

‣ allows for frozen-core, all-electron potentials

‣ can calculate all core wave functions for excited atomic configurations to whatever accuracy required

‣ can freeze holes in core states – allows for a fully 3D multi-centred approach of charge states which are integers (no average atom approximation for ionization)

‣ charge state independent of temperature/density: can model equilibrium (pick the right temperature for the mean chosen ionization) or non-equilibrium systems (in terms of the ionization), includes some

fluctuations (ensemble of integer charge states is simulated directly),

‣ can reconstruct the “real” valence density everywhere, including on ionic cores, where overlap with core wave functions becomes relevant. No spherical symmetry assumed.

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Calculate the IPD from first principles - Roadmap

Generate pool of excited-

configuration PAW potentials with frozen inner shell core-hole states

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Calculate the IPD from first principles - Roadmap

Input: ion structure (crystal), charge state distribution and temperature

FT-DFT calculation:

minimize energy under constraint of potentials

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Identical to above, but with additional 1 K-shell hole in ion of interest

Calculate the IPD from first principles - Roadmap

FT-DFT calculation:

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Calculate the IPD from first principles - Roadmap

FT-DFT calculation:

K-edge via free-energy diﬀerence

Vinko, Ciricosta & Wark, Nature Comm 5, 3533 (2014)

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Calculate the IPD from first principles - Roadmap

FT-DFT calculation:

K-edge via free-energy diﬀerence

IPD!

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What do we calculate?

Density of States

Energy

Valence 2p states

2s states 1s states

Populations selected in creation of the potential Calculated in the single atom limit (radial DFT, Hartree-Fock-Dirac, etc.)

Core

Determined from 3D DFT calculation: the lowest energy configuration possible given our choice of the core (still formally ground- state)

Populations determined by chosen

temperature via the Fermi-Dirac distribution 3s states

Continuum

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-20 -10 0 10 Energy (eV)

0 5 10 15 20 25

Density of States (states/eV/cell)

Al continuum structure at diﬀerent temperatures

5 10 15 20 25

Density of States (states/eV/cell)

100 eV

75 eV

50 eV

25 eV

10 eV

1 eV

7⁺ 6⁺ 6⁺

6⁺

Calculation box:

Atomic-like 3s state

(Electron density 3.75 x10

²³

cm

^-3

)

100 eV 75 eV 50 eV 25 eV 10 eV 1 eV

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K-shell spectroscopy of Hot Dense Aluminium: 3+

IV

1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680

1475 1500 1525 1550 1575 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825

L shell

Continuum

K shell

0

1800

1700

1600

1500

DFT

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K-shell spectroscopy of Hot Dense Aluminium: 6+

VII

0

1800

1700

1600

1500

DFT

1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1475

1500 1525 1550 1575 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825

K shell L shell

Continuum

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3 4 5 6 7 8 9

Charge state

0 50 100 150 200 250

Ionization Potential Depr ession (eV)

Experiment SP (a.a.) EK (a.a.)

Comparison of calculations with experiment: Aluminium

3 4 5 6 7 8 9

Charge state

0 50 100 150 200 250

Ionization Potential Depr ession (eV)

Experiment

SP (a.a.)

EK (a.a.)

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3 4 5 6 7 8 9 0

50 100 150 200 250

Ionization Potential Depr ession (eV)

Experiment SP (a.a.) EK (a.a.)

DFT (a.a., Gamma point)

Comparison of calculations with experiment: Aluminium

3 4 5 6 7 8 9

0 50 100 150 200 250

Ionization Potential Depr ession (eV)

Experiment

SP (a.a.)

EK (a.a.)

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3 4 5 6 7 8 9

Charge state

0 50 100 150 200 250

Ionization Potential Depr ession (eV)

Experiment SP (a.a.) EK (a.a.)

DFT (a.a., Gamma point) DFT (a.a., p-like)

Comparison of calculations with experiment: Aluminium

3 4 5 6 7 8 9

Charge state

0 50 100 150 200 250

Ionization Potential Depr ession (eV)

Experiment SP (a.a.) EK (a.a.)

Nature Comm 5, 3533 (2014)

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DFT method reproduces experimental IPDs

Electron interactions with ions and other electrons remains strong in the conditions generated on LCLS.

At solid density, continuum states are formed due to the interaction of M-shell states which form the conduction band (tight-binding picture).

0 0.5 1 1.5 2 2.5

0 2 4 6 8 10

Atomic core density 7+

Atomic valence density 7+

Average valence density DFT 1 eV

DFT 10 eV DFT 25 eV DFT 50 eV DFT 75 eV DFT 100 eV

r (a0) Electron density 4πr2 ρ(r) (a0-1 )

1s² 2s² 2p²

Aluminium

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Atomic bound-bound transitions can be a good approximation for bound-free edge

K: 1s² L: 2s² 2p⁶ M: 3s² 3p¹

Isolated Al Atom Al Atom in metal

Atomic Continuum

Continuum in dense system

Higher states

Conduction band

IPD

K-M bound bound transitions

model the K-edge

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Outline

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The experiment at the Linac Coherent Light Source X-ray Free-Electron Laser

X-ray spectrometer: K-alpha emission Al around 1500 eV LCLS pulse

Photon energy: 1460–1830 eV Pulse length < 60 fs

Pulse Energy ~1.5 mJ Bandwidth ~ 0.4%

Diode Bragg

crystal

1 micron thick Al sample

Vinko et al., Nature 482, 59 (2012) Ciricosta et al., PRL 109, 065002 (2012)

CCD

Peak Intensity ~10¹⁷W cm^-2

(60)

Saturable absorption at 1.5 - 1.8 keV ~ 10

¹⁷

Wcm

^-2

Saturable absorption occurs due to ‘burning through’ of charge states such that the K-edge of the highly charged ions lies above the FEL photon energy. Thus at the higher photon energies we need to wait until the end of the pulse to lower the absorption, and it is not so eﬀective.

Note: the mechanism is diﬀerent from that in the XUV, where we were

‘beating’ a longer (40-fsec) Auger rate.

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Evolution of charge states and opacity

FEL energy is 1670 eV, just below k-edge of 7+

Peak x-ray intensity 20% of peak x-ray intensity

Final absorption will be the integral over time and weighted intensities.

(62)

Outline

(63)

If the FEL photon energy is too low, no K-α generated Ionized Al: e.g. 6+

K: 1s² L: 2s² 2p³

(64)

If the FEL photon energy is too low, no K-α generated Ionized Al: e.g. 6+

K: 1s² L: 2s² 2p³

Not quite true!

(65)

IV V VI VII VIII Line

K-edge region Emission only due to collisions from lower charge state(s)

Experimental measurement of collisional ionization

rates on LCLS

(66)

1500 1550 1600 1650 1700 1750 1800 Photon energy (eV)

1^x10⁴ 1^x10⁵ 1^x10⁶ 1x10⁷

Emission (phot/eV/sterad)

IVV VIVII

IV V VI VII VIII Line

Clear steps in emission are

observed below the K-edge of a given charge state!

Experimental measurement of collisional ionization

rates on LCLS

(67)

Process that produces K

α

emission

K2Lμ

K1Lμ

K2Lμ-1

K2Lμ-2

K-shell

Photoionization

Auger

LCLS Pulse

Radiative

Kα photon

(68)

Process that produces K

α

emission

K2Lμ

K1Lμ

K2Lμ-1

K2Lμ-2

K-shell

Photoionization

Auger

LCLS Pulse

Radiative

Kα photon

L-shell collisional

ionization ^K²^L^μ-1

(69)

Process that produces K

α

emission

K2Lμ

K1Lμ

K2Lμ-1

K2Lμ-2

K-shell

Photoionization

Auger

LCLS Pulse

Radiative

Kα photon

L-shell collisional

ionization ^K²^L^μ-1

K-edge is too high for photoionization:

no emission!

(70)

Process that produces K

α

emission

K2Lμ

K1Lμ

K2Lμ-1

K2Lμ-2

K-shell

Photoionization

Auger

LCLS Pulse

Radiative

Kα photon

K1Lμ-1

K2Lμ-2

K2Lμ-3

Auger

Radiative

Kα photon L-shell collisional

ionization

(71)

Process that produces K

α

emission

K2Lμ

K1Lμ

K2Lμ-1

K2Lμ-2

K-shell

Photoionization

Auger

LCLS Pulse

Radiative

Kα photon

K1Lμ-1

K2Lμ-2

K2Lμ-3

Auger

Radiative

ionization ^K¹^L^μ-2

K2Lμ-3

K2Lμ-4

Auger

Radiative

ionization

(72)

Collisions occur within Auger lifetime of K-shell

1590 eV 1630 eV

10² 10³ 10⁴ 10⁵ 10⁶

Intensity (a.u.)

IV V VI VII VIII

Intensity (a.u.)

IV V VI VII VIII

Experiment Simulation

a b

Above-edge Below-edge Above-edge Below-edge

Kβ

Collisions Collisions

(73)

We can model the eﬀect of stronger/weaker collisions

1550 1575 1600 1625 1650 1675 1700

Photon Energy (eV)

0.01 0.1 1 10

Emission Intensity (a.u.)

Experiment Sim 0.2xCR Sim 1.0xCR Sim 3.0xCR Sim 5.0xCR

V VI VII

VIII IV

Rates are underestimated by a factor between 3 and 5!

First measure of collisional ionisation rate in a dense plasma.

Nature Comm 6, 6397 (2015)

The Physics of Solid Density Plasmas Created by Intense X-Ray Free Electron Lasers